HARMONY FOR MATH NERDS


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        So, the "relationship of frequencies in a scale is logarithmic." Two pitches an octave apart will create a frequency twice the frequency of the lower note.  For example, middle A's frequency is about 440 Hz, so an A played an octave higher will produce vibrations of 880 Hz.  Now back to the simple integer relationships mentioned above.  Octaves have 2:1 ratios.  The next simple integer relationship in a scale "is the interval of an octave and a fifth."  The ratio of an octave to a fifth is 3:2 (ex: E is 660 Hz to A's 440 Hz).  

        "The ratio of the note an octave and a fifth to the root is 3:1 because the fifth an octave higher is twice the frequency of the original fifth, and 3/2 (the fifth) x 2 (the octave) is 3" (Benner).  The ratio is 3:1. 

        In terms of the note-to-note ratios, a chord made by a fifth and a major third is more consonant (this is a hard term to describe in words - it's sort of like dominance in a sound verses submission) than a minor triad which is made of a fifth and a minor third.  Because of the increased consonance between major versus minor triads, they seem more fulfilling to our emotions.

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